FIN303 midterm 2: ch 8

What are the two primary types of investment risk?

Stand-alone risk and portfolio risk.

Stand-alone risk

if holding 1 particular asset

Portfolio risk

holding portfolio

• market risk → holding well diversified market portfolio

Investment risk

related to the probability of earning a low or negative actual return.

How does return fluctuation affect the riskiness of an investment?

The greater the chance of lower than expected, or negative returns, the riskier the investment (a higher dispersion or fluctuation from the mean/expected rate of return)

• risk fluctuates a lot

• higher risk

What is a probability distribution?

A listing of all possible outcomes and the probability of each outcome occurring.

If Firm X and Firm Y both have an expected return of 15%, but Firm Y has a higher standard deviation than Firm X, which firm is riskier?

Firm Y, because a higher standard deviation indicates greater dispersion of returns and higher stand-alone risk.

• firm x → narrower distribution (better)

• firm y → wider distribution (carries higher risk, dispersion higher than the mean)

• try to minimize risk given same expected rate of return

standard deviation

how return fluctuates around mean (dispersion from mean)

cyclical

moves with economy; good economy = less bad sales

• market portfolio (MP) = cyclical

Hypothetical Investment Alternatives (with Five Possible Outcomes for Five Assets)

probability distribution. 1 of 5 states must occur because sum of probabilities = 100

Why Is T-bill Return Independent of The Economy?

T-bills will return the promised 3.0%, regardless of the economy (no matter what)

Do T bills Promise A Completely Risk-free Return?

No, they are still exposed to inflation. Although very little unexpected inflation is likely to occur over such a short period of time.

(IP does not = 0), still suffer inflation risk

• T-bills are also risky in terms of reinvestment risk.

In what specific sense are U.S. Treasury bills risk-free?

in the default sense of the word. DRP = 0, LP=MRP= 0

What is a cyclical stock?

High Tech: Moves with the economy and has a positive correlation. This is typical.

What is a countercyclical stock?

Collections: Is countercyclical with the economy and has a negative correlation. This is unusual.

• moves against, in opposite direction, of economy

• some of risks may offset

• if put collections in portfolio, can offset risks; collections may have positive returns

higher sigma

wider distribution, higher risk (dispersion from mean)

Why is choosing an investment solely based on the highest expected return insufficient?

Evaluating expected return alone fails to account for the investment’s risk.

What type of risk does standard deviation (σi) measure?

Total risk, also called stand-alone risk.

How does a larger standard deviation (σi) relate to expected return probability?

the lower the probability that actual returns will be close to expected returns (a higher dispersion from the mean)

• associated with a wider probability distribution of returns (fluctuates more on both sides)

Why is Collections, with an expected return of 1.2% and standard deviation of 11.2%, dominated by T-bills, with an expected return of 3.0% and standard deviation of 0.0%?

T-bills offer a higher expected return with lower stand-alone risk.

Why is U.S. Rubber, with an expected return of 7.3% and standard deviation of 18.8%, dominated by the Market Portfolio, with an expected return of 8.0% and standard deviation of 15.2%?

The Market Portfolio offers a higher expected return with lower stand-alone risk.

What does the Coefficient of Variation measure?

A standardized measure of dispersion about the expected value that shows risk per unit of return.

• relative measurement → how much risk have to take

In general, is a larger or smaller Coefficient of Variation preferred?

A smaller CV is preferred (better investment)

If Investment A and Investment B have identical standard deviations, but Investment A has a lower expected return than B, which investment is riskier?

Investment A, because it has a higher CV, meaning more risk per unit of return, and a higher probability of losses.

Sharpe Ratio

an alternative measure of stand-alone risk. It looks at excess return (in excess of the risk free rate) relative to risk

Sharpe Ratio: Excess return

an asset’s expected return minus the risk-free rate

Sharpe Ratio: how is risk measured?

by the standard deviation of the asset’s returns.

Sharpe Ratio: risk-free asset will have?

a Sharpe ratio of 0.

• in general, the higher the sharpe ratio, the better the investment

Investor Attitude towards Risk: Risk premium

the difference between the return on a risky asset and a riskless asset, which serves as compensation for investors to hold riskier securities.

Investor Attitude towards Risk: Risk aversion

assumes investors dislike risk and require higher rates of return to encourage them to hold riskier securities

portfolio’s expected return

a weighted average of the returns of the portfolio’s component assets.

• portfolio can reduce risk

Standard deviation is a bit tricky and requires?

that a new probability distribution for the portfolio returns be constructed.

General Comments about Risk

• σp ~35% for an average stock.

• Most stocks are positively (though not perfectly) correlated with the market (i.e., ρ between 0 and 1).

  • perfect = 1 to 1 relationship

• Combining stocks in a portfolio generally lowers risk.

Creating A Portfolio: Beginning with One Stock and Adding Randomly Selected Stocks to Portfolio

• σp decreases as stocks are added, because they would not be perfectly correlated with the existing portfolio.

• Expected return of the portfolio would remain relatively constant.

• Eventually the diversification benefits of adding more stocks dissipates (after about 40 stocks), and for large stock portfolios, σp tends to converge to ≈ 20%.

  • can’t add more stocks to diversify risk

As the number of stocks in the portfolio increases, what happens to portfolio risk?

portfolio risk decreases; but it can never decrease to zero

What is diversifiable risk?

The firm-specific portion of a security’s stand-alone risk that can be eliminated through proper portfolio diversification. (company’s specific risk)

What is market risk?

a portion of a security’s stand-alone risk that cannot be eliminated through diversification. Measured by beta; non-diversifiable risk

If an investor chooses to hold a one-stock portfolio (doesn’t diversify), would the investor be compensated for the extra risk he/she bears? (everything in 1 basket)

NO!

• Stand-alone risk is not important to a well-diversified investor.

• No compensation should be earned for holding unnecessary, diversifiable risk.

• in diverse portfolio, only facing market risk

• compensating only if holding asset with this amount of market risk

• rewarded only for market risk; specific risk = no reward

Capital Asset Pricing Model (CAPM)

Model linking risk and required returns. CAPM suggests that there is a Security Market Line (SML) that states that a stock’s required return equals the risk-free return plus a risk premium that reflects the stock’s risk after diversification.

• help you to price asset

• non-diversifiable risk, not standard deviation

• no risk = risk free rate

CAPM Explanation

• The model relates the required rate of return to the market risk

• Capital Asset Pricing Model (CAPM) → ri= rRF + ( rM - rRF ) bi compared to y = a + bx

• where, ri is the required rate of return (y-axis or dependent variable) on stock i;

• rRF is the risk-free rate (intercept);

• (rm – rRF) is the market risk premium (slope);

• b i is the market risk for stock i (x-axis or independent variable);

• and (rm – rRF) is the risk premium of stock i

CAPM Security Market Line equation

• ri=rRF+(rM-rRF)bi

• y=a+b*x

• bi = beta (measurement of market risk)

What is the primary conclusion of CAPM regarding stock riskiness?

The relevant risk of a stock is its contribution to the riskiness of a well-diversified portfolio, or market risk.

Beta

Measures a stock’s market risk and shows a stock’s volatility relative to the market. Indicates how risky a stock is if the stock is held in a well-diversified portfolio

• sensitivity → if market changes, what happens to stock

• increased beta = good when market goes up; when market drops, lose more

• high beta = high return with additional reward

• slope = beta estimation/coefficient

If beta = 1.0

the security is just as risky as the average stock (or the overall market)

If beta > 1.0

the security is riskier than the average (riskier than the overall market)

If beta < 1.0

the security is less risky than the average (less risky than the overall market)

Most stocks have betas in the range of?

0.5 to 1.5 (in theory Beta is negative, in practice very rare)

Can The Beta of A Security Be Negative?

Yes, if the correlation between Stock i and the market is negative (i.e., pi.m < 0)

• If the correlation is negative, the regression line would slope downward, and the beta would be negative.

• However, a negative beta is highly unlikely

• market higher = stock moves slower)

Calculating Beta: Well-diversified investors are primarily concerned with?

how a stock is expected to move relative to the market in the future.

Calculating Beta: Without a crystal ball to predict the future, analysts are forced to rely on historical data. A typical approach to estimate beta is?

to run a regression of the security’s past returns against the past returns of the market.

Calculating Beta: The slope of the regression line is defined as?

the beta coefficient for the security.

Market Risk Premium

• Additional return over the risk-free rate needed to compensate investors for assuming an average amount of risk (market risk).

• Its size depends on the perceived risk of the stock market and investors’ degree of risk aversion.

• It varies over time, but most estimates suggest that it ranges between 4% and 8% per year.

What if your stock has a beta of 1.5?

According to CAPM, you should earn 1.5 times of the market risk premium.

• take market risk → get additional 5% return

beta of a portfolio

the weighted average of each of the stock’s betas

required return of a portfolio

weighted average of each of the stock’s required returns.

If investors raised inflation expectations by 3%, what would happen to the SML?

a parallel shift by 3% without the change in slope

• if market interest rate rises, see parallel shift (intercept changes; slopes stays same because it’s market risk premium)

If investors’ risk aversion increased, causing the market risk premium to increase by 3%, what would happen to the SML?

a change in slope without the change in intercept; investors are getting more risk averse

• slope = market risk premium

  • investors getting more risk adverse; asking for more than market risk premium (more risk adverse)